Polytope of Type {20,10,4}

s0 := (  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(101,151)(102,155)(103,154)(104,153)(105,152)(106,171)(107,175)(108,174)(109,173)(110,172)(111,166)(112,170)(113,169)(114,168)(115,167)(116,161)(117,165)(118,164)(119,163)(120,162)(121,156)(122,160)(123,159)(124,158)(125,157)(126,176)(127,180)(128,179)(129,178)(130,177)(131,196)(132,200)(133,199)(134,198)(135,197)(136,191)(137,195)(138,194)(139,193)(140,192)(141,186)(142,190)(143,189)(144,188)(145,187)(146,181)(147,185)(148,184)(149,183)(150,182)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)(301,351)(302,355)(303,354)(304,353)(305,352)(306,371)(307,375)(308,374)(309,373)(310,372)(311,366)(312,370)(313,369)(314,368)(315,367)(316,361)(317,365)(318,364)(319,363)(320,362)(321,356)(322,360)(323,359)(324,358)(325,357)(326,376)(327,380)(328,379)(329,378)(330,377)(331,396)(332,400)(333,399)(334,398)(335,397)(336,391)(337,395)(338,394)(339,393)(340,392)(341,386)(342,390)(343,389)(344,388)(345,387)(346,381)(347,385)(348,384)(349,383)(350,382);;
s1 := (  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)(  8,105)(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)( 32,126)( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)( 56,152)( 57,151)( 58,155)( 59,154)( 60,153)( 61,172)( 62,171)( 63,175)( 64,174)( 65,173)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,162)( 72,161)( 73,165)( 74,164)( 75,163)( 76,182)( 77,181)( 78,185)( 79,184)( 80,183)( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,197)( 87,196)( 88,200)( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,187)( 97,186)( 98,190)( 99,189)(100,188)(201,307)(202,306)(203,310)(204,309)(205,308)(206,302)(207,301)(208,305)(209,304)(210,303)(211,322)(212,321)(213,325)(214,324)(215,323)(216,317)(217,316)(218,320)(219,319)(220,318)(221,312)(222,311)(223,315)(224,314)(225,313)(226,332)(227,331)(228,335)(229,334)(230,333)(231,327)(232,326)(233,330)(234,329)(235,328)(236,347)(237,346)(238,350)(239,349)(240,348)(241,342)(242,341)(243,345)(244,344)(245,343)(246,337)(247,336)(248,340)(249,339)(250,338)(251,357)(252,356)(253,360)(254,359)(255,358)(256,352)(257,351)(258,355)(259,354)(260,353)(261,372)(262,371)(263,375)(264,374)(265,373)(266,367)(267,366)(268,370)(269,369)(270,368)(271,362)(272,361)(273,365)(274,364)(275,363)(276,382)(277,381)(278,385)(279,384)(280,383)(281,377)(282,376)(283,380)(284,379)(285,378)(286,397)(287,396)(288,400)(289,399)(290,398)(291,392)(292,391)(293,395)(294,394)(295,393)(296,387)(297,386)(298,390)(299,389)(300,388);;
s2 := (  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195)(201,226)(202,227)(203,228)(204,229)(205,230)(206,246)(207,247)(208,248)(209,249)(210,250)(211,241)(212,242)(213,243)(214,244)(215,245)(216,236)(217,237)(218,238)(219,239)(220,240)(221,231)(222,232)(223,233)(224,234)(225,235)(251,276)(252,277)(253,278)(254,279)(255,280)(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)(272,282)(273,283)(274,284)(275,285)(301,326)(302,327)(303,328)(304,329)(305,330)(306,346)(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)(314,344)(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)(322,332)(323,333)(324,334)(325,335)(351,376)(352,377)(353,378)(354,379)(355,380)(356,396)(357,397)(358,398)(359,399)(360,400)(361,391)(362,392)(363,393)(364,394)(365,395)(366,386)(367,387)(368,388)(369,389)(370,390)(371,381)(372,382)(373,383)(374,384)(375,385);;
s3 := (  1,201)(  2,202)(  3,203)(  4,204)(  5,205)(  6,206)(  7,207)(  8,208)(  9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)( 16,216)( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)( 24,224)( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)( 32,232)( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)( 40,240)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)( 48,248)( 49,249)( 50,250)( 51,251)( 52,252)( 53,253)( 54,254)( 55,255)( 56,256)( 57,257)( 58,258)( 59,259)( 60,260)( 61,261)( 62,262)( 63,263)( 64,264)( 65,265)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,271)( 72,272)( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)( 80,280)( 81,281)( 82,282)( 83,283)( 84,284)( 85,285)( 86,286)( 87,287)( 88,288)( 89,289)( 90,290)( 91,291)( 92,292)( 93,293)( 94,294)( 95,295)( 96,296)( 97,297)( 98,298)( 99,299)(100,300)(101,301)(102,302)(103,303)(104,304)(105,305)(106,306)(107,307)(108,308)(109,309)(110,310)(111,311)(112,312)(113,313)(114,314)(115,315)(116,316)(117,317)(118,318)(119,319)(120,320)(121,321)(122,322)(123,323)(124,324)(125,325)(126,326)(127,327)(128,328)(129,329)(130,330)(131,331)(132,332)(133,333)(134,334)(135,335)(136,336)(137,337)(138,338)(139,339)(140,340)(141,341)(142,342)(143,343)(144,344)(145,345)(146,346)(147,347)(148,348)(149,349)(150,350)(151,351)(152,352)(153,353)(154,354)(155,355)(156,356)(157,357)(158,358)(159,359)(160,360)(161,361)(162,362)(163,363)(164,364)(165,365)(166,366)(167,367)(168,368)(169,369)(170,370)(171,371)(172,372)(173,373)(174,374)(175,375)(176,376)(177,377)(178,378)(179,379)(180,380)(181,381)(182,382)(183,383)(184,384)(185,385)(186,386)(187,387)(188,388)(189,389)(190,390)(191,391)(192,392)(193,393)(194,394)(195,395)(196,396)(197,397)(198,398)(199,399)(200,400);;
poly := Group([s0,s1,s2,s3]);;

F := FreeGroup("s0","s1","s2","s3");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  s3 := F.4;;  
rels := [ s0*s0, s1*s1, s2*s2, s3*s3, s0*s2*s0*s2, 
s0*s3*s0*s3, s1*s3*s1*s3, s1*s2*s3*s2*s1*s2*s3*s2, 
s2*s3*s2*s3*s2*s3*s2*s3, s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

s0 := Sym(400)!(  2,  5)(  3,  4)(  6, 21)(  7, 25)(  8, 24)(  9, 23)( 10, 22)( 11, 16)( 12, 20)( 13, 19)( 14, 18)( 15, 17)( 27, 30)( 28, 29)( 31, 46)( 32, 50)( 33, 49)( 34, 48)( 35, 47)( 36, 41)( 37, 45)( 38, 44)( 39, 43)( 40, 42)( 52, 55)( 53, 54)( 56, 71)( 57, 75)( 58, 74)( 59, 73)( 60, 72)( 61, 66)( 62, 70)( 63, 69)( 64, 68)( 65, 67)( 77, 80)( 78, 79)( 81, 96)( 82,100)( 83, 99)( 84, 98)( 85, 97)( 86, 91)( 87, 95)( 88, 94)( 89, 93)( 90, 92)(101,151)(102,155)(103,154)(104,153)(105,152)(106,171)(107,175)(108,174)(109,173)(110,172)(111,166)(112,170)(113,169)(114,168)(115,167)(116,161)(117,165)(118,164)(119,163)(120,162)(121,156)(122,160)(123,159)(124,158)(125,157)(126,176)(127,180)(128,179)(129,178)(130,177)(131,196)(132,200)(133,199)(134,198)(135,197)(136,191)(137,195)(138,194)(139,193)(140,192)(141,186)(142,190)(143,189)(144,188)(145,187)(146,181)(147,185)(148,184)(149,183)(150,182)(202,205)(203,204)(206,221)(207,225)(208,224)(209,223)(210,222)(211,216)(212,220)(213,219)(214,218)(215,217)(227,230)(228,229)(231,246)(232,250)(233,249)(234,248)(235,247)(236,241)(237,245)(238,244)(239,243)(240,242)(252,255)(253,254)(256,271)(257,275)(258,274)(259,273)(260,272)(261,266)(262,270)(263,269)(264,268)(265,267)(277,280)(278,279)(281,296)(282,300)(283,299)(284,298)(285,297)(286,291)(287,295)(288,294)(289,293)(290,292)(301,351)(302,355)(303,354)(304,353)(305,352)(306,371)(307,375)(308,374)(309,373)(310,372)(311,366)(312,370)(313,369)(314,368)(315,367)(316,361)(317,365)(318,364)(319,363)(320,362)(321,356)(322,360)(323,359)(324,358)(325,357)(326,376)(327,380)(328,379)(329,378)(330,377)(331,396)(332,400)(333,399)(334,398)(335,397)(336,391)(337,395)(338,394)(339,393)(340,392)(341,386)(342,390)(343,389)(344,388)(345,387)(346,381)(347,385)(348,384)(349,383)(350,382);
s1 := Sym(400)!(  1,107)(  2,106)(  3,110)(  4,109)(  5,108)(  6,102)(  7,101)(  8,105)(  9,104)( 10,103)( 11,122)( 12,121)( 13,125)( 14,124)( 15,123)( 16,117)( 17,116)( 18,120)( 19,119)( 20,118)( 21,112)( 22,111)( 23,115)( 24,114)( 25,113)( 26,132)( 27,131)( 28,135)( 29,134)( 30,133)( 31,127)( 32,126)( 33,130)( 34,129)( 35,128)( 36,147)( 37,146)( 38,150)( 39,149)( 40,148)( 41,142)( 42,141)( 43,145)( 44,144)( 45,143)( 46,137)( 47,136)( 48,140)( 49,139)( 50,138)( 51,157)( 52,156)( 53,160)( 54,159)( 55,158)( 56,152)( 57,151)( 58,155)( 59,154)( 60,153)( 61,172)( 62,171)( 63,175)( 64,174)( 65,173)( 66,167)( 67,166)( 68,170)( 69,169)( 70,168)( 71,162)( 72,161)( 73,165)( 74,164)( 75,163)( 76,182)( 77,181)( 78,185)( 79,184)( 80,183)( 81,177)( 82,176)( 83,180)( 84,179)( 85,178)( 86,197)( 87,196)( 88,200)( 89,199)( 90,198)( 91,192)( 92,191)( 93,195)( 94,194)( 95,193)( 96,187)( 97,186)( 98,190)( 99,189)(100,188)(201,307)(202,306)(203,310)(204,309)(205,308)(206,302)(207,301)(208,305)(209,304)(210,303)(211,322)(212,321)(213,325)(214,324)(215,323)(216,317)(217,316)(218,320)(219,319)(220,318)(221,312)(222,311)(223,315)(224,314)(225,313)(226,332)(227,331)(228,335)(229,334)(230,333)(231,327)(232,326)(233,330)(234,329)(235,328)(236,347)(237,346)(238,350)(239,349)(240,348)(241,342)(242,341)(243,345)(244,344)(245,343)(246,337)(247,336)(248,340)(249,339)(250,338)(251,357)(252,356)(253,360)(254,359)(255,358)(256,352)(257,351)(258,355)(259,354)(260,353)(261,372)(262,371)(263,375)(264,374)(265,373)(266,367)(267,366)(268,370)(269,369)(270,368)(271,362)(272,361)(273,365)(274,364)(275,363)(276,382)(277,381)(278,385)(279,384)(280,383)(281,377)(282,376)(283,380)(284,379)(285,378)(286,397)(287,396)(288,400)(289,399)(290,398)(291,392)(292,391)(293,395)(294,394)(295,393)(296,387)(297,386)(298,390)(299,389)(300,388);
s2 := Sym(400)!(  6, 21)(  7, 22)(  8, 23)(  9, 24)( 10, 25)( 11, 16)( 12, 17)( 13, 18)( 14, 19)( 15, 20)( 31, 46)( 32, 47)( 33, 48)( 34, 49)( 35, 50)( 36, 41)( 37, 42)( 38, 43)( 39, 44)( 40, 45)( 56, 71)( 57, 72)( 58, 73)( 59, 74)( 60, 75)( 61, 66)( 62, 67)( 63, 68)( 64, 69)( 65, 70)( 81, 96)( 82, 97)( 83, 98)( 84, 99)( 85,100)( 86, 91)( 87, 92)( 88, 93)( 89, 94)( 90, 95)(106,121)(107,122)(108,123)(109,124)(110,125)(111,116)(112,117)(113,118)(114,119)(115,120)(131,146)(132,147)(133,148)(134,149)(135,150)(136,141)(137,142)(138,143)(139,144)(140,145)(156,171)(157,172)(158,173)(159,174)(160,175)(161,166)(162,167)(163,168)(164,169)(165,170)(181,196)(182,197)(183,198)(184,199)(185,200)(186,191)(187,192)(188,193)(189,194)(190,195)(201,226)(202,227)(203,228)(204,229)(205,230)(206,246)(207,247)(208,248)(209,249)(210,250)(211,241)(212,242)(213,243)(214,244)(215,245)(216,236)(217,237)(218,238)(219,239)(220,240)(221,231)(222,232)(223,233)(224,234)(225,235)(251,276)(252,277)(253,278)(254,279)(255,280)(256,296)(257,297)(258,298)(259,299)(260,300)(261,291)(262,292)(263,293)(264,294)(265,295)(266,286)(267,287)(268,288)(269,289)(270,290)(271,281)(272,282)(273,283)(274,284)(275,285)(301,326)(302,327)(303,328)(304,329)(305,330)(306,346)(307,347)(308,348)(309,349)(310,350)(311,341)(312,342)(313,343)(314,344)(315,345)(316,336)(317,337)(318,338)(319,339)(320,340)(321,331)(322,332)(323,333)(324,334)(325,335)(351,376)(352,377)(353,378)(354,379)(355,380)(356,396)(357,397)(358,398)(359,399)(360,400)(361,391)(362,392)(363,393)(364,394)(365,395)(366,386)(367,387)(368,388)(369,389)(370,390)(371,381)(372,382)(373,383)(374,384)(375,385);
s3 := Sym(400)!(  1,201)(  2,202)(  3,203)(  4,204)(  5,205)(  6,206)(  7,207)(  8,208)(  9,209)( 10,210)( 11,211)( 12,212)( 13,213)( 14,214)( 15,215)( 16,216)( 17,217)( 18,218)( 19,219)( 20,220)( 21,221)( 22,222)( 23,223)( 24,224)( 25,225)( 26,226)( 27,227)( 28,228)( 29,229)( 30,230)( 31,231)( 32,232)( 33,233)( 34,234)( 35,235)( 36,236)( 37,237)( 38,238)( 39,239)( 40,240)( 41,241)( 42,242)( 43,243)( 44,244)( 45,245)( 46,246)( 47,247)( 48,248)( 49,249)( 50,250)( 51,251)( 52,252)( 53,253)( 54,254)( 55,255)( 56,256)( 57,257)( 58,258)( 59,259)( 60,260)( 61,261)( 62,262)( 63,263)( 64,264)( 65,265)( 66,266)( 67,267)( 68,268)( 69,269)( 70,270)( 71,271)( 72,272)( 73,273)( 74,274)( 75,275)( 76,276)( 77,277)( 78,278)( 79,279)( 80,280)( 81,281)( 82,282)( 83,283)( 84,284)( 85,285)( 86,286)( 87,287)( 88,288)( 89,289)( 90,290)( 91,291)( 92,292)( 93,293)( 94,294)( 95,295)( 96,296)( 97,297)( 98,298)( 99,299)(100,300)(101,301)(102,302)(103,303)(104,304)(105,305)(106,306)(107,307)(108,308)(109,309)(110,310)(111,311)(112,312)(113,313)(114,314)(115,315)(116,316)(117,317)(118,318)(119,319)(120,320)(121,321)(122,322)(123,323)(124,324)(125,325)(126,326)(127,327)(128,328)(129,329)(130,330)(131,331)(132,332)(133,333)(134,334)(135,335)(136,336)(137,337)(138,338)(139,339)(140,340)(141,341)(142,342)(143,343)(144,344)(145,345)(146,346)(147,347)(148,348)(149,349)(150,350)(151,351)(152,352)(153,353)(154,354)(155,355)(156,356)(157,357)(158,358)(159,359)(160,360)(161,361)(162,362)(163,363)(164,364)(165,365)(166,366)(167,367)(168,368)(169,369)(170,370)(171,371)(172,372)(173,373)(174,374)(175,375)(176,376)(177,377)(178,378)(179,379)(180,380)(181,381)(182,382)(183,383)(184,384)(185,385)(186,386)(187,387)(188,388)(189,389)(190,390)(191,391)(192,392)(193,393)(194,394)(195,395)(196,396)(197,397)(198,398)(199,399)(200,400);
poly := sub<Sym(400)|s0,s1,s2,s3>;

poly<s0,s1,s2,s3> := Group< s0,s1,s2,s3 | s0*s0, s1*s1, s2*s2, 
s3*s3, s0*s2*s0*s2, s0*s3*s0*s3, s1*s3*s1*s3, 
s1*s2*s3*s2*s1*s2*s3*s2, s2*s3*s2*s3*s2*s3*s2*s3, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;